Usually, quantum mechanics is considered as the prototype of a probabilistic theory. In contrast to statistical mechanics, dice throwing, and roulette game, quantum mechanical probability statements cannot be reduced to causally determined individual events, whose explicit calculation is, however, too complicated for all practical purposes. Even hypothetically, one must not assume that quantum mechanical events were determined in principle and merely computationally intractable, since that assumption would lead to probabilistic predictions which contradict quantum mechanics. Hence, the title of this article seems somewhat surprising at first glance, and in particular it seems difficult to connect a probability free quantum mechanics with the work of John von Neumann.